The publications and other materials referred to in this Specification are for convenience numerically referenced in the following text and grouped under the heading "References."
Optical fiber systems have the potential for extremely high communication rates. Existing monomode fiber systems have demonstrated transmission rates as high as 8 Gbits/second. Although quite large, this is still only a small fraction of the available bandwidth. Full utilization of the low-loss window in the 1.3-1.5 micrometer (.mu.m) region leads to a potential bandwidth on the order of 30 THz. The limitation on the data transmission, thus, becomes the modulator, and as modulator bandwidths increase, we can expect to see larger and larger transmission rates.
Digital communication system that utilize even a fraction of the potential bandwith available in a single-mode fiber must work with pulses in the femtosecond range.
There are certain disadvantages to working with such ultrashort pulses:
Short pulses have broad spectral widths.
With broad spectra, group velocity dispersion (GVD) can become the limiting factor in the available bandwidth of an optical fiber communications system. Short pulses, at quite modest energies, quickly lead to peak intensities sufficient to cause nonlinear effects in fibers. The confining nature of the optical waveguide is ideal for providing long interaction lengths for such phenomena. These nonlinear effects (e.g. self-phase modulation, Raman generation) generally lead to the creation of excess spectral content (even possibly the existence of pulses which did not exist at the input) which aggravate the GVD problem and further limit the useful bandwidth.
A number of solutions to the first problem have been described:
Manufacture of ultrabroadband waveguides through the use of novel refractive index profiles.
Operation at the wavelength of zero material dispersion. At this wavelength, the first order dispersion vanishes and the second order dispersion dominates.
Optical pulse equalization using positive-negative dispersion compensation. This involves splicing together fibers with different dispersion characteristics to minimize the first order dispersion.
Marcuse has discussed these last two ideas thoroughly, along with limitations due to other sources of dispersion such as polarization mode dispersion.
All of these solutions to the GVD problem strive to keep a pulse together--in and of itself this is a desirable feature of any communications system. This, however, has an adverse effect when one looks at the limitations that this imposes on the average power handling capacities of an optical fiber.
Consider the limitations imposed on a digital communication system by the nonlinear processes of Brillouin scattering, Raman scattering, and self-phase modulation. In order to simplify the analysis somewhat, we restrict ourselves to a digital communication system and ignore any effects of GVD within the fiber.
The growth of a stimulated Brillouin and Raman signal has been examined by R. G. Smith. Expressions for the critical peak pump (input) power are derived. When P&gt;P.sub.CRIT, significant energy transfer to the stimulated Brillouin or Raman signal occurs.
For Brillouin scattering: ##EQU1## where
A=x-sectional area of fiber (cm.sup.2)
.alpha..sub.p =exponential loss coefficient (cm.sup.-1)
.gamma..sub.o =Brillouin gain (cm/w)
For Raman scattering a similar result holds: ##EQU2## where .gamma..sub.o is now the Raman gain. A typical loss coefficient at .about.1.3 .mu.m is 0.5 dB/km (0.115/km). The Brillouin gain for quartz is .about.3.times.10.sup.-9 cm/W. The Raman gain is .about.1.8.times.10.sup.-11 cm/W. Using these numbers in the above expressions (for a core area of 10.sup.-7 cm.sup.2) we get values of ##EQU3## However, because the Brillouin gain bandwidth is only .about.50 MHz wide, we must multiply this by (.DELTA..nu..sub.PUMP)/(.DELTA..nu..sub.BRILL). This makes ##EQU4## and we will no longer consider Brillouin scattering; the Raman process, having a very large bandwidth (.DELTA..nu..sub.RAMAN &gt;&gt;.DELTA..nu..sub.PUMP) will be the dominant effect of the two. The critical power for self-phase modulation has been defined as: ##EQU5##
where n.sub.2 is the nonlinear part of the index of refraction (1.1.times.10.sup.-13 esu). For the same parameters as above, this evaluates to ##EQU6## for a 10 km fiber.
At peak powers of 15 mW and 100 mW, a 100 fs pulse has energies of 1.5 and 10 femtojoules (fJ), respectively. Even at a 10 GHz repetition rate, the average powers are still only at the milliwatt level.
The onset of any of these effects is a hindrance to accurate transmission of data, and leads to new (and undesirable) spectral content. In addition, the low powers place stringent requirements on splicing losses and necessitate frequent use of expensive, electronic repeating stations.